Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

Uncertainty quantification for linear inverse problems remains a challenging task, especially for problems with a very large number of unknown parameters (e.g., dynamic inverse problems) and for problems where computation of the square root and inverse of the prior covariance matrix are not feasible. This work exploits Krylov subspace methods to develop and analyze new techniques for large‐scale uncertainty quantification in inverse problems. In this work, we assume that generalized Golub‐Kahan‐based methods have been used to compute an estimate of the solution, and we describe efficient methods to explore the posterior distribution. In particular, we use the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and we provide theoretical results that quantify the accuracy of the approximate posterior covariance matrix and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback‐Liebler divergence. We present two methods that use the preconditioned Lanczos algorithm to efficiently generate samples from the posterior distribution. Numerical examples from dynamic photoacoustic tomography demonstrate the effectiveness of the described approaches.     

In vivo metabolic investigation of silodosin using UHPLC–QTOF–MS/MS and in silico toxicological screening of its metabolites

Silodosin (SLD) is a novel α1‐adrenoceptor antagonist which has shown promising clinical efficacy and safety in patients with benign prostatic hyperplasia (BPH). However, lack of information about metabolism of SLD prompted us to investigate metabolic fate of SLD in rats. To identify in vivo metabolites of SLD, urine, feces and plasma were collected from Sprague–Dawley rats after its oral administration. The samples were prepared using an optimized sample preparation approach involving protein precipitation followed by solid‐phase extraction and then subjected to LC/HR‐MS/MS analysis. A total of 13 phase I and six phase II metabolites of SLD have been identified in rat urine which includes hydroxylated, N‐dealkylated, dehydrogenated, oxidative, glucosylated, glucuronide and N‐sulphated metabolites, which are also observed in feces. In plasma, only dehydrogenated, N‐dealkylated and unchanged SLD are observed. The structure elucidation of metabolites was done by fragmentation in MS/MS in combination with HRMS data. The potential toxicity profile of SLD and its metabolites were predicted using TOPKAT software and most of the metabolites were proposed to show a certain degree of skin sensitization and occular irritancy. Copyright © 2016 John Wiley & Sons, Ltd.     

High temperature drop calorimetry measurements of enthalpy increment in Ti–xTa (x=5, 10, 15, 20 mass%) alloys

The enthalpy increment for a series of Ti–xTa (x=5, 10, 15, 20 mass%) alloys, having α(hcp)+β(bcc) two phase microstructure has been measured using inverse drop calorimetry in the temperature range 463–1257 K. The studies clearly revealed the occurrence of α→β diffusional phase transformation. Both the α→β transformation onset temperatures and the measured transformation enthalpy Δ⁰H_tr^α→β exhibit progressively lower values with increasing Ta content. It is found that the measured enthalpy in the transformation region is constituted of two principal contributions namely, (i) the enthalpy due to untransformed α and coexisting β phases and (ii) the transformation enthalpy due to α→β phase change. Since the fractional extent of α→β transformation varies continuously with temperature, the measured enthalpy variation in the transformation domain has been modeled using Kolmogorov–Johnson–Mehl–Avrami formalism for the diffusional transformation kinetics. The thermodynamic quantities for all the alloys have been derived.     

2-hydroxymethyl-4-[5-(4-methoxyphenyl)-3-trifluoromethyl-1H-1-pyrazolyl]-1-benzenesulfonamide (DRF-4367): an orally active COX-2 inhibitor identified through pharmacophoric modulation

Analogs of 1,5-diarylpyrazoles with a novel pharmacophore at N1 were designed, synthesized and evaluated for the in-vitro cyclooxygenase (COX-1/COX-2) inhibitory activity. The variations at/around position-4 of the C-5 phenyl ring in conjunction with a CF3 and CHF2 groups at C-3 exhibited a high degree of potency and selectivity index (SI) for COX-2 inhibition. The in-vivo evaluation of these potent compounds with a few earlier ones indicated the 4-OMe-phenyl analog and the 4-NHMe-phenyl analog with a CF3, and the 4-OEt-phenyl analog with a CHF2 group at C-3 to possess superior potency than celecoxib. In addition to its impressive anti-inflammatory, antipyretic, analgesic and anti-arthritic properties, compound (DRF-4367) was found to possess an excellent pharmacokinetic profile, gastrointestinal (GI) safety in the long-term arthritis study and COX-2 potency in human whole blood assay. Thus, compound was selected as an orally active anti-inflammatory candidate for pre-clinical evaluation.     

The Chemistry of L-Ascorbic and D-Isoascorbic Acids. 3: Efficient Syntheses of Pure R- and S- 1,2-O-Isopropylidene-1,2,4-Butanetriols1

Both enantiomers of 1,2-0-isopropylidene-1,2,4-butanetriol were prepared by two different and simple methods starting from readily available L-ascorbic and D-isoascorbic acids.     

Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen–Loève expansion

We describe randomized algorithms for computing the dominant eigenmodes of the generalized Hermitian eigenvalue problem Ax = λBx, with A Hermitian and B Hermitian and positive definite. The algorithms we describe only require forming operations Ax,Bx and B^?1x and avoid forming square roots of B (or operations of the form, B^1/2x or B^?1/2x). We provide a convergence analysis and a posteriori error bounds and derive some new results that provide insight into the accuracy of the eigenvalue calculations. The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B^?1A decay rapidly. A randomized algorithm for the generalized singular value decomposition is also provided. Finally, we demonstrate the performance of our algorithm on computing an approximation to the Karhunen–Loève expansion, which involves a computationally intensive generalized Hermitian eigenvalue problem with rapidly decaying eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.